DE 10 2004 025 638 A1 describes a brake system for motor vehicles. On activation of the brake pedal, a first piston of the brake system can be moved into an inner chamber, encased by a second piston, with an elastic element. Parallel movement of the second piston with the first piston causes a pressure on a third piston of a master cylinder. As an alternative to the direct braking by the vehicle driver in the master brake cylinder, by means of the pressure transmitted via the second piston to the third piston via a hydraulic pressure provision module with a pressure medium storage reservoir and a first pump to fill the pressure medium storage reservoir, a pressure can be created in an intermediate chamber between the second piston and the third piston. By means of the created pressure, the third piston can be moved at least partly into the master brake cylinder and the second piston out of the master brake cylinder. Arranged on the master brake cylinder are two brake circuits, each with a second and a third pump. The brake system therefore has a first pump motor to operate the first pump and a second pump motor to operate the second pump and the third pump.